This protocol serves to extend the successful treatment for HIV positive patients beyond the endpoints provided by the Phase 2b TaiMed Biologics-sponsored protocol TMB202 (entitled "A Phase 2b Randomized, Double-Blinded, 48-Week, Multicenter, Dose-Response Study of Ibalizumab Plus an Optimized Background Regimen in Treatment-Experienced Patients Infected with HIV-1 (Amended to 24 Week Study)"), for 24 weeks. Ibalizumab may be administered beyond 24 weeks under this protocol as supply permits and patients continue to demonstrate virologic response.